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arXiv · 2504.02774

Component-wise Krasnosel'skii type fixed point theorem in product spaces and applications

Laura M Fernández-Pardo·Jorge Rodríguez-López
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Abstract

We present a version of Krasnosel'skii fixed point theorem for operators acting on Cartesian products of normed linear spaces, under cone-compression and cone-expansion conditions of norm type. Our approach, based on the fixed point index theory in cones, guarantees the existence of a coexistence fixed point - that is, one with nontrivial components. As an application, we prove the existence of periodic solutions with strictly positive components for a system of second-order differential equations. In particular, we address cases involving singular nonlinearities and hybrid terms, characterized by sublinear behavior in one component and superlinear behavior in the other.

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Laura M Fernández-Pardo, Jorge Rodríguez-López. 2025-04-03. Component-wise Krasnosel'skii type fixed point theorem in product spaces and applications. https://arxiv.org/abs/2504.02774

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